[论文解读] Neural Networks for Fast Optimisation in Model Predictive Control: A Review

Camilo González, Houshyar Asadi+2 more|arXiv (Cornell University)|Sep 6, 2023

Advanced Control Systems Optimization被引用 11

一句话总结

本综述评估基于神经网络的优化（NNBO）以替代 MPC 求解器，对方法进行分类，比较保证与加速，并突出存在的差距与未来方向。

ABSTRACT

Model Predictive Control (MPC) is an optimal control algorithm with strong stability and robustness guarantees. Despite its popularity in robotics and industrial applications, the main challenge in deploying MPC is its high computation cost, stemming from the need to solve an optimisation problem at each control interval. There are several methods to reduce this cost. This survey focusses on approaches where a neural network is used to approximate an existing controller. Herein, relevant and unique neural approximation methods for linear, nonlinear, and robust MPC are presented and compared. Comparisons are based on the theoretical guarantees that are preserved, the factor by which the original controller is sped up, and the size of problem that a framework is applicable to. Research contributions include: a taxonomy that organises existing knowledge, a summary of literary gaps, discussion on promising research directions, and simple guidelines for choosing an approximation framework. The main conclusions are that (1) new benchmarking tools are needed to help prove the generalisability and scalability of approximation frameworks, (2) future breakthroughs most likely lie in the development of ties between control and learning, and (3) the potential and applicability of recently developed neural architectures and tools remains unexplored in this field.

研究动机与目标

• 为 MPC 的 NNBO 方法（LMPC、NMPC、RMPC）提供一个分类体系。
• 总结在不同保证条件下用神经网络替代 MPC 求解器的方法。
• 对 NNBO 框架的速度提升、问题规模和在实际应用中的适用性进行基准比较。
• 识别 NNBO 在 MPC 方面的差距、挑战与未来潜在研究方向。

提出的方法

• 按 MPC 类型（LMPC、NMPC、RMPC）及保留的保证对 NNBO 方法进行分类。
• 解释基于模仿学习的 NNBO 框架以及后处理/验证策略。
• 总结无保证、概率保证与严格保证之间的权衡。
• 比较案例研究在问题规模、时间步长与报道的加速（仿真与机器人领域）的情况。
• 提供一个选择指南，帮助根据 MPC 类型和应用场景选择 NNBO 方法。
• 突出差距并提出在控制-学习整合方面的未来研究方向。

Figure 1: Typical implementation of NNBO to replace an MPC controller.

实验结果

研究问题

• RQ1 在 LMPC、NMPC 和 RMPC 的场景下，存在哪些用于替换 MPC 求解器的 NNBO 框架？
• RQ2 这些 NNBO 方法保留哪些保证（无、概率性还是严格？；在何种条件下？）
• RQ3 这些方法在问题规模、时域纲要、计算加速方面的表现如何，且对实际系统的泛化能力如何？

主要发现

Ref	L	Core Concept	Guaranties	n_x	n_y	n_u	N_p	N_c	Speed up	Validation
Åkesson et al. (2005)	1b	Train shallow NN to imitate LMPC using RMSE loss function, remove setpoint tracking error manually by zeroing NN outputs for setpoints.	None	2	1	1	20	20	4,000 - 5,000x	Sim
Drgoňa et al. (2018)	1c	Train DNN with MSE loss to imitate MPC. DNN inputs defined via PCA and manual selection.	None	286	6	6	22	22	7.6x	Sim
Kumar et al. (2018)	1a	Approximation of MPC with NN that combines LSTM and DNN. LSTM learns dependence on past actions while DNN learns dependence on current states.	None	4	1	1	-	-	-	Sim
Zhang et al. (2020)	2a	Fit DNN to primal and dual problems thereby enabling online constraint satisfaction check. If violations occur, call backup controller.	Probabilistic optimality with ability to check constraint satisfaction online.	4	3	3	3	3	10x	Robot
Chen et al. (2022)	3a	Train DNN to initialise active set solver and thereby reduce iterations to convergence.	Recursive feasibility and asymptotic stability.	36	36	9	50	50	2x	Sim
Chen et al. (2018)	3b	Project the outputs of an approximate DNN solver onto feasible output sets such that recursive feasibility is maintained. Train the DNN with policy gradient RL instead of supervised learning.	Recursive feasibility of inputs and states.	4	4	2	10	10	-	Sim
Karg and Lucia (2020a)	2c	Paper provides requirements for exact approximation of Explicit LMPC with DNN.	All EMPC guarantees for exact fits. Only constraint satisfaction for approximations.	4	1	1	10	10	-	Sim
Karg and Lucia (2020b)	2c	Verify input and state constraint satisfaction by solving a MILP that performs output range analysis on DNN ReLU approximation of solver, modify the approximation to behave like an LQR controller near the equilibrium point.	Input and state constraint satisfaction and stability.	2	1	1	3	3	-	Sim
Fabiani and Goulart (2022)	2c	Derives conditions based on worst-case error and Lipschitz constant under which DNN ReLU approximations are stable. Formulates MILPs to calculate such quantities.	Optimality, stability, and recursive feasibility.	8	8	3	5	5	-	Sim

• 仍需要用于 NNBO 在 MPC 中的基准测试工具和泛化性测试。
• 未来的突破很可能来自控制与学习的更深度整合。
• 在 NNBO 的 MPC 领域，新神经网络结构与学习工具的潜力尚未被充分开发。
• 在报道的案例中，与精确 MPC 相比，NNBO 方法的加速范围从适度（约 2x）到非常大（成千上万倍）不等。
• 一些方法通过对偶/原始模仿和备用控制器提供概率性或约束满足保证；其他方法则没有正式保证。
• 成功的演示很大一部分发生在仿真中，实际部署较少。

Figure 2: Block diagram of typical implementation and components of MPC solution.